2-2:30 Talk by Heather Battey
Title: Distributed estimation and hypothesis testing with statistical guarantees.
Abstract: In many applications, the rows of an $(n x d)$ data matrix are distributed across multiple machines, either due to the experimental design or due to the impracticalities associated with storing and manipulating large scale data on a single machine. This results in $k$ smaller data sets of dimensions $((n/k) x d)$, where $k$ is the number of machines. How large can $k$ be relative to $n$ and $d$ such that an aggregate of the $k$ statistics delivers the same statistical performance as the practically infeasible full sample statistic? I will discuss this question in the context of hypothesis testing and estimation in linear and generalised linear models, giving particular focus to the more challenging case of $d>n$. In the context of hypothesis testing, statistical guarantees are distributional, whilst for estimation they come in the form of minimax rates of convergence.
2:30-3pm Talk by Din-Houn Lau (Imperial)
Title:The chopthin algorithm for resampling
Abstract: Resampling is a standard and important step in particle filters and more generally sequential Monte Carlo methods. In this presentation, we introduce a new method, called chopthin, for resampling weighted particles. In contrast to standard resampling methods the algorithm does not produce a set of equally weighted particles; instead it merely enforces an upper bound on the ratio between the weights. A simulation study shows that the chopthin algorithm consistently outperforms standard resampling methods. The algorithms chops up particles with large weight and thins out particles with low weight, hence its name. It implicitly guarantees a lower bound on the effective sample size. The algorithm can be implemented very efficiently, making it practically useful. We show that the expected computational effort is linear in the number of particles. Implementations for C++, R (on CRAN), Python and for Matlab are available. (http://arxiv.org/abs/1502.07532)